In the classical situation where \(q_n = 1\)  (at most),
all scenarios in Definition REF  REF  coincide,
extending the assumption \(d_1^2 \min (\theta _1 - n - \theta _1) \rightarrow \infty \) 
which is commonly found in the change point testing literature,
see [1]}.
However, when \(q_n > 1\) , they truly reflect different scenarios:
Proceeding from (i) to (iii) enlarges the associated parameter space,
and thus (iii) provides the most general setting in which to
investigate the detection power of a segmentation procedure.
While most of the literature deals with the homogeneous setting (see Section REF ),
it is often too restrictive and does not permit large frequent jumps
alternate with small jumps over long segments – a situation naturally embedded in the multiscale setting.
In Definition REF  REF ,
the multiscale localisation rate relates the difficulty in accurate localisation of each change point
to the size of the corresponding jump.
